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Dividing Decimals

A child comes across with numbers as soon as he/she starts understanding things. Numbers are everywhere. The study of numbers is not always very simple. There is an important branch of mathematics known as number theory in which students study about different kinds of numbers and various axioms on those.

There are different types of numbers, such as - real numbers, natural numbers, whole numbers, decimal number, rational numbers, irrational numbers, integers. Here, we will learn about decimal number. Decimals are the numbers which have a decimal point in between. Any proper fraction or improper fraction can be expressed in terms of decimals. The part of the fraction which is obtained when the numerator of the fraction is divided by the denominator of the fraction is expressed as decimals. Get quality fraction help here.

Any decimal number has ten as its base. Example : $\frac{5}{10}$ = 0.2.

Various arithmetic operations can be imposed on decimal numbers. Students can learn Dividing decimals online. They can learn the different types of decimal division, like how to divide decimals by decimals and how to divide decimals with whole numbers. In order to understand about division of decimals in detail, refer the following information given below in this page.

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How to Divide Decimals

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Below are the rules for how to divide decimals -

Rule 1 : First we begin with given problem values.
Rule 2 : And then we divide the given problems without decimals
Rule 3 : After that put decimal places for that numbers.
Rule 4 : Finally specify the solution.

Below you can see the examples for how do you divide decimals -

Solved Examples

Question 1: Divide 4.8 by 0.6
Solution:

Step 1: First we begin with $\frac{4.8}{0.6}$

Step 2: and Then we divide without decimal points, we get

                          = $\frac{48}{6}$

                          = 8

Step 3: and then we put decimal places

                  4.8 have one decimal place.

                  0.6 has one decimal place.
Step 4: Final answer has two decimal places 8



Correct answer is 8
Question 2: Divide 6.6 by 6
Solution:

Step 1: First we begin with $\frac{6.6}{6}$

Step 2: and Then we divide without decimal points, we get

                          = $\frac{66}{6}$

                          = 11

 Step 3: and then we put decimal places

              6.6 have one decimal place.

                6 has no decimal place.

 Step 4: Final answer has one decimal places 1.1



Correct answer is 1.1
Question 3: Divide 1.2 by 0.3
Solution:

Step 1: First we begin with $\frac{1.2}{0.3}$

Step 2: and Then we divide without decimal points, we get

                        = $\frac{12}{3}$

                         = 4

Step 3: and then we put decimal places

             1.2 has one decimal place.

             0.3 have one decimal place.
Step 4: Final answer has one decimal places 4.



Correct answer is 4

Dividing Decimals by Whole Numbers

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For dividing decimal by whole, place the decimal point in the quotient directly above the decimal point in the dividend. Then follow the normal division method what we do with whole numbers division. After the division is over we get the quotient, place the decimal point in the place based on the decimal point in the dividend given.

Below are the examples of how to divide decimals by whole numbers -

Solved Examples

Question 1: Division of decimals by whole numbers $\frac{18.8}{2}$
Solution:
Given the divisor is 2 and the dividend is 18.8

First estimate: $\frac{18}{2}$ = 9.  Put the decimal point.           

                     9.4      
              2 | 18.8
                     18                  Divide like a whole numbers.
                     8 
                     8     
                     0    


Correct answer is quotient is 9.4 and remainder is 0.
Question 2: Division of decimals by whole numbers $\frac{30.3}{3}$
Solution:

Given the divisor is 3 and the dividend is 30.3

First estimate: $\frac{30}{3}$ = 10.   Put the decimal point.      

                    10.1      
          3 | 30.3   
               - 30                  Divide like a whole numbers.
                   3
                   3     
                   0   



Correct answer is quotient is 10.1 and remainder is 0

Dividing Decimals by Decimals

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Dividing Decimals by decimal numbers can be explained by the following example. Students can learn by observing the steps followed as to how to divide decimals with decimals.

Step 1 : Convert the decimal number you are dividing into whole number first, that is done by shifting the decimal point to the extreme right.

Step 2 : Following the steps explained for division of a decimal number by whole number.

Step 3 : Now change the decimal point position to right of the value obtained in Step 2 that many times you shifted right in the step 1.

Now see the example of how to divide decimals by decimals -

Solved Example

Question: Divide 6.6 by 2.2
Solution:

Step 1 : Make 2.2 as 22 by shifting decimal point to right one time, so that the decimal number becomes whole number.

Step 2 : We will not consider the decimal value in the numerator and apply Long division method.

    03
22) 66
      66
       0

We can now place the decimal value for the below problem. 

      0.3
22 )6.6
Step 3 : Now shift the decimal point one time to right in the above result i.e., by shifting decimal point of 0.3 to the right one time answer is 3.


Correct answer is 3

Practice Problems

Question 1: 8.3 ÷ 2.1
Question 2: 7.3 ÷ 5.5
Question 3: 7.1 ÷ 6
Question 4: 5.8 ÷ 3

How to do Long Division with Decimals

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Here we are going to see how to do long division with decimals. The dividing decimal is containing quotient, remainder and divider. This is used to dividing the given decimals. The condition for dividing positive and negative decimals also applies to division with rational numbers. Consider that to divide by nonzero number, multiply by the reciprocal of that number.

Solved Example

Question: Solve 855.8 ÷ 2.
Solution:
2 )855.8( 427.9
     8       
     5
     4      
     15
     14    
       18
       18  
        0   
Steps to show how to do long division with decimals:

Step 1: In the given problem the dividend is 855.8 and the divisor is 2

Step 2: Now we are going to divide 855.8 by 2, we take the first number of the divisor. Since 2 is less than 8 we can stop with 8

Step 3: The divisor 2 is multiplied with the quotient 4 and gives the result of 8, so when we subtract 8 by 8 we get the remainder of 0.

Step 4: The remainder we have is 0, so we bring down 5.

Step 5: Now 2 is multiplied with 2 to get 4. When 4 subtracted with 5 we get 1 so we bring 5 down.

Step 6: When 2 is multiplied with 7 we will get 14 so when 14 subtracted from 15 we will get 1.There is a decimal point present in the dividend. So we can take that and put it in the quotient and proceed with the problem.

Step 7: Now we bring 8 down. When 2 multiplied with 9 we will get 19. When we subtract 18 by 18 we get 0. So the remainder is 0

Step 8: By solving 855.8 ÷ 2 we get the remainder as 0 and the quotient is 427.9 . This is how to do long division with decimals.


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